A200541 Product of Fibonacci and tribonacci numbers: a(n) = A000045(n+1)*A000073(n+2).

1, 1, 4, 12, 35, 104, 312, 924, 2754, 8195, 24386, 72576, 215991, 642785, 1912960, 5693016, 16942573, 50421592, 150056090, 446571180, 1329008590, 3955167387, 11770690808, 35029911168, 104250013425, 310251009501, 923315841860, 2747814245904, 8177573467339, 24336691577000

Offset: 0

Author

Paul D. Hanna, Nov 18 2011

Keywords

• nonn

Comments

Limit a(n+1)/a(n) = (sqrt(5)+1)/2 * (1+(19+3*sqrt(33))^(1/3)+(19-3*sqrt(33))^(1/3))/3 = 2.9760284849940...

Examples

			G.f.: A(x) = 1 + x + 4*x^2 + 12*x^3 + 35*x^4 + 104*x^5 + 312*x^6 + 924*x^7 + 2754*x^8 +...+ A000045(n+1)*A000073(n+2)*x^n +...
where tribonacci numbers (A000073) begin:
[1,1,2,4,7,13,24,44,81,149,274,504,927,1705,3136,5768,10609,...],
and Fibonacci numbers (A000045) begin:
[1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,...].
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (1,4,5,2,-1,1).

Crossrefs

Cf. A001582, A000045, A000073.

Programs

Mathematica

Module[{nn=30,fs,ts},fs=Fibonacci[Range[nn]];ts=LinearRecurrence[{1,1,1},{1,1,2},nn];Times@@@Thread[{fs,ts}]] (* or *) LinearRecurrence[ {1,4,5,2,-1,1},{1,1,4,12,35,104},30] (* Harvey P. Dale, Dec 14 2016 *)

PARI

{a(n)=polcoeff((1-x^2-x^3)/(1-x-4*x^2-5*x^3-2*x^4+x^5-x^6 +x*O(x^n)),n)}

PARI

{A000073(n)=polcoeff(x^2/(1-x-x^2-x^3+x^3*O(x^n)),n)}
{a(n)=fibonacci(n+1)*A000073(n+2)}

Formula

G.f.: (1 - x^2 - x^3) / (1 - x - 4*x^2 - 5*x^3 - 2*x^4 + x^5 - x^6).